R. M. Benito

Efficiency of human activity on information spreading on Twitter

Understanding the collective reaction to individual actions is key to effectively spread information in social media. In this work we define efficiency on Twitter, as the ratio between the emergent spreading process and the activity employed by the user. We characterize this property by means of a quantitative analysis of the structural and dynamical patterns emergent from human interactions, and show it to be universal across several Twitter conversations. We found that some influential users efficiently cause remarkable collective reactions by each message sent, while the majority of users must employ extremely larger efforts to reach similar effects. Next we propose a model that reproduces the retweet cascades occurring on Twitter to explain the emergent distribution of the user efficiency. The model shows that the dynamical patterns of the conversations are strongly conditioned by the topology of the underlying network. We conclude that the appearance of a small fraction of extremely efficient users results from the heterogeneity of the followers network and independently of the individual user behavior.

An extended formalism for preferential attachment in heterogeneous complex networks

In this paper we present a framework for the extension of the Barabasi-Albert model to heterogeneous complex networks. We define a class of heterogeneous preferential attachment models where node properties are described by fixed states in an arbitrary space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the degree distributions in heterogeneous preferential attachment networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in the presence of heterogeneity.

Measuring political polarization: Twitter shows the two sides of Venezuela

We say that a population is perfectly polarized when divided in two groups of the same size and opposite opinions. In this paper, we propose a methodology to study and measure the emergence of polarization from social interactions. We begin by proposing a model to estimate opinions in which a minority of influential individuals propagate their opinions through a social network. The result of the model is an opinion probability density function. Next, we propose an index to quantify the extent to which the resulting distribution is polarized. Finally, we apply the proposed methodology to a Twitter conversation about the late Venezuelan president, Hugo Chávez, finding a good agreement between our results and offline data. Hence, we show that our methodology can detect different degrees of polarization, depending on the structure of the network.

Local frequency analysis and the structure of classical phase space of the LiNC/LiCN molecular system

The phase space structure of a generic Hamiltonian model, describing the vibrational dynamics of the LiNC/LiCN molecular system, is studied using a frequency analysis method. The results obtained for the regular region constitute a true parametrization of the corresponding invariant tori on which the trajectories are located. By performing the frequency analysis locally, much richer information about chaotic trajectories is obtained, since it clearly reveals the dynamical characteristics of trajectory fragments hidden behind the t→∞ ergodic property.

Signatures of homoclinic motion in quantum chaos.

Homoclinic motion plays a key role in the organization of classical chaos in Hamiltonian systems. In this Letter, we show that it also imprints a clear signature in the corresponding quantum spectra. By numerically studying the fluctuations of the widths of wave functions localized along periodic orbits we reveal the existence of an oscillatory behavior that is explained solely in terms of the primary homoclinic motion. Furthermore, our results indicate that it survives the semiclassical limit.

Quantum manifestations of saddle-node bifurcations

Abstract We show that the periodic orbits originating from a saddle-node bifurcation have a profound influence on the topology of the vibrational wavefunctions of the LiNC/LiCN molecular system described by a realistic and complex potential energy surface. The underlying classical structures (manifolds) are examined in detail.

EMERGENCE OF MULTISCALING IN HETEROGENEOUS COMPLEX NETWORKS

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the threshold model, a preferential attachment model where the affinity between node states biases the attachment probabilities of links. We show that the degree densities exhibit a power-law multiscaling which points to a signature of heterogeneity in preferential attachment networks. This translates into a power-law scaling in the degree distribution, whose exponent depends on the specific form of heterogeneity in the attachment mechanism.

SADDLE-NODE BIFURCATIONS IN THE LINC/LICN MOLECULAR SYSTEM : CLASSICAL ASPECTS AND QUANTUM MANIFESTATIONS

A classical‐quantum correspondence study of a saddle‐node bifurcation in a realistic molecular system is presented. The relevant classical structures (periodic orbits and manifolds) and its origin are examined in detail. The most important conclusion of this study is that, below the bifurcation point, there exists an infinite sequence of precursor orbits, which mimic for a significant period of time the (future) saddle‐node orbits. These structures have a profound influence in the quantum mechanics of the molecule and several vibrational wave functions of the system present a strong localization along the saddle‐node periodic orbits. A striking result is that this scarring effect also takes place well below the bifurcation energy, which constitutes a manifestation of the so‐called ‘‘ghost’’ orbits in configuration and phase space. This localization effect has been further investigated using wave packet dynamics.

Saddle point resonances in a bound system with classical chaos

Abstract The saddle point region of a highly non-linear, non-separable bound Hamiltonian system, representing an isomerization process for the LiCN molecule, is found to induce a resonance-like behavior in both quantum and classical dynamics. The origin and relaxation mechanism of the resonances are given.

Semiclassical quantization of fragmented tori: Application to saddle-node states of LiNC/LiCN

A new implementation of the EBK method for the semiclassical quantization of partially destroyed tori is presented. The application to the calculation of some quantum states of the LiNC/LiCN molecule which are influenced by a saddle-node bifurcation is discussed. In this quantization surrogates of invariant tori, computed using gap filling saddle-node orbits, are used. These orbits are obtained from a very detailed study of the islands around islands structure existing in the relevant classical phase space region.